SVM Kernels Indepth Intuition And Practical Explanation¶

In [1]:
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
%matplotlib inline
In [2]:
x = np.linspace(-5.0,5.0, 100)
y = np.sqrt(10**2 - x**2)
In [3]:
x.shape
Out[3]:
(100,)
In [4]:
y.shape
Out[4]:
(100,)
In [5]:
y = np.hstack([y,-y])
x = np.hstack([x,-x])
In [6]:
x.shape
Out[6]:
(200,)
In [7]:
y.shape
Out[7]:
(200,)
In [8]:
x1 = np.linspace(-5.0, 5.0, 100)
y1 = np.sqrt(5**2 - x1**2)
y1=np.hstack([y1,-y1])
x1=np.hstack([x1,-x1])
In [9]:
y1.shape
Out[9]:
(200,)
In [10]:
x1.shape
Out[10]:
(200,)
In [11]:
plt.scatter(y,x)
plt.scatter(y1,x1)
Out[11]:
<matplotlib.collections.PathCollection at 0x25935ba63d0>
In [ ]:
In [12]:
# Change a DataFrame (x,y)
df1 = pd.DataFrame(np.vstack([y,x]).T,columns = ['X1','X2'])
df1['Y'] = 0

# Change a DataFrame (x1,y1)
df2 = pd.DataFrame(np.vstack([y1,x1]).T,columns = ['X1','X2'])
df2['Y'] = 1
In [13]:
#append the two dataframe(df1,df2)
df = df1.append(df2)
df.head()

C:\Users\dines\AppData\Local\Temp\ipykernel_13024\1397825995.py:2: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  df = df1.append(df2)
Out[13]:
X1 X2 Y
0 8.660254 -5.00000 0
1 8.717792 -4.89899 0
2 8.773790 -4.79798 0
3 8.828277 -4.69697 0
4 8.881281 -4.59596 0
In [14]:
x = df.iloc[:,:2]
y = df['Y']
In [15]:
x.head()
Out[15]:
X1 X2
0 8.660254 -5.00000
1 8.717792 -4.89899
2 8.773790 -4.79798
3 8.828277 -4.69697
4 8.881281 -4.59596
In [16]:
y
Out[16]:
0      0
1      0
2      0
3      0
4      0
      ..
195    1
196    1
197    1
198    1
199    1
Name: Y, Length: 400, dtype: int64
In [17]:
#Split the dataset into train_test
from sklearn.model_selection import train_test_split
x_train,x_test,y_train,y_test = train_test_split(x,y,test_size = 0.25,random_state = 0)
In [18]:
x_train.shape
Out[18]:
(300, 2)
In [19]:
y_train.shape
Out[19]:
(300,)
In [20]:
x_test.shape
Out[20]:
(100, 2)
In [21]:
x_test.shape
Out[21]:
(100, 2)
In [ ]:

Base_Model building¶

In [22]:
from sklearn.svm import SVC
In [23]:
cls = SVC(kernel = "rbf")
cls.fit(x_train,y_train)
Out[23]:
SVC()
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SVC()
In [24]:
#Evaluation Metrics
from sklearn.metrics import accuracy_score
y_pred = cls.predict(x_test)
accuracy_score(y_test,y_pred)
Out[24]:
1.0
In [ ]:
In [25]:
df.head()
Out[25]:
X1 X2 Y
0 8.660254 -5.00000 0
1 8.717792 -4.89899 0
2 8.773790 -4.79798 0
3 8.828277 -4.69697 0
4 8.881281 -4.59596 0
In [ ]:

Polynomial Kernel¶

In [26]:
# We need to find components for the Polynomical Kernel
#X1,X2,X1_square,X2_square,X1*X2
df['X1_Square']= df['X1']**2
df['X2_Square']= df['X2']**2
df['X1*X2'] = (df['X1'] *df['X2'])
df.head()
Out[26]:
X1 X2 Y X1_Square X2_Square X1*X2
0 8.660254 -5.00000 0 75.000000 25.000000 -43.301270
1 8.717792 -4.89899 0 75.999898 24.000102 -42.708375
2 8.773790 -4.79798 0 76.979390 23.020610 -42.096467
3 8.828277 -4.69697 0 77.938476 22.061524 -41.466150
4 8.881281 -4.59596 0 78.877155 21.122845 -40.818009
In [27]:
df['X1'].shape
Out[27]:
(400,)
In [28]:
# Independent and Dependent features
x = df[['X1','X2','X1_Square','X2_Square','X1*X2']]
y = df['Y']
In [29]:
y
Out[29]:
0      0
1      0
2      0
3      0
4      0
      ..
195    1
196    1
197    1
198    1
199    1
Name: Y, Length: 400, dtype: int64
In [30]:
#train_test_split
x_train,x_test,y_train,y_test = train_test_split(x,y,test_size = 0.25,random_state = 0)
In [31]:
x_train.shape
Out[31]:
(300, 5)
In [32]:
y_train.shape
Out[32]:
(300,)
In [33]:
#import poltly
import plotly.express as px

fig = px.scatter_3d(df, x="X1", y ="X2",z="X1*X2",color = 'Y')

fig.show()
In [34]:
fig = px.scatter_3d(df, x="X1_Square", y ="X1_Square",z="X1*X2",color = 'Y')

fig.show()
In [35]:
classifier = SVC(kernel="linear")
classifier.fit(x_train, y_train)
y_pred = classifier.predict(x_test)
accuracy_score(y_test, y_pred)
Out[35]:
1.0
In [ ]:
In [ ]: